Estimation of the intensity of non-homogeneous point processes via wavelets

Author(s)

Simon de Miranda, Jose Carlos ^[1] ; Morettin, Pedro A. ^[1]

Affiliation

^[1] Inst Math & Stat, Dept Stat, BR-05311970 Sao Paulo - Brazil

• Document type: Journal article
• Source: ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS; v. 63, n. 6, p. 1221-1246, DEC 2011.
• Web of Science Citations: 2

Abstract

In this article we consider the problem of estimating the intensity of a non-homogeneous point process on the real line. The approach used is via wavelet expansions. Estimators of the intensity are proposed and their properties are studied, including the case of thresholded versions. Properties of the estimators for non-homogeneous Poisson processes follow as special cases. An application is given for the series of daily Dow Jones indices. Extensions to more general settings are also indicated. (AU)

• FAPESP's process: 08/51097-6 - Time Series, Dependence Analysis and Applications
• Grantee: Pedro Alberto Morettin
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 03/10105-2 - Temporal series, analysis of dependency and applications in actuarial science and finance
• Grantee: Pedro Alberto Morettin
• Support Opportunities: PRONEX Research - Thematic Grants